Question: Ben is 15 years older than Michael. Four years ago, Ben was 4 times as old as Michael. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Ben and Michael. Let Ben's current age be $b$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $b = m + 15$ Four years ago, Ben was $b - 4$ years old, and Michael was $m - 4$ years old. The information in the second sentence can be expressed in the following equation: $b - 4 = 4(m - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = m + 15$ . Substituting this into our second equation, we get the equation: $(m + 15)$ $-$ $4 = 4(m - 4)$ which combines the information about $m$ from both of our original equations. Simplifying both sides of this equation, we get: $m + 11 = 4 m - 16$ Solving for $m$ , we get: $3 m = 27$ $m = 9$.